We need to user service "messenger" service, which will store the message in the session and fetch during the next request.

Get instance of messenger service

# 1. Standard way to get messenger service, in case you want to pass it using dependency injection.
$messenger = \Drupal::service("messenger");

# 2. Fast way to use helper function.

$messenger = \Drupal::messenger();

Also in the form object or controller we don't have include it using dependency injection. We can us directly 

$messenger = $this->messenger();

Methods

1. Add message. Allows to send a message of any type, the second parameter accepts the type

$meesenger->addMessage(t('Your message.'), MessengerInterface::TYPE_WARNING);

But in most of the cases it is better to use directly specific method

2. Add status

$messenger->addStatus(t('Your message'));

3. Add warning

$messenger->addWarning(t('Your message'));

4. Add error

$messenger->addError(t('Your message'));